ABSTRACT The cultivation of onion Allium cepa L. is of extreme economic importance globally, and, because of this, research must be constantly updated in order to increase productivity. This study was designed to estimate the optimal plot size, sample size and number of repetitions for experiments evaluating variables in the onion crop. Uniformity tests were carried in the years 2016 and 2017 in the experimental area of the Crop Science Department at Universidade Federal de Santa Maria, Santa Maria (RS), Brazil. Each plant was considered a basic experimental unit. Bulb mass, bulb height, and bulb diameter were measured for each basic experimental unit. The optimal plot size, sample size, and number of repetitions were estimated by the method of maximum curvature of the variation coefficient. For onion culture, the optimal plot size to evaluate the bulb mass, bulb height and bulb diameter is eight, six and six, respectively. The optimal sample size for evaluating the bulb mass of the onion crop is six plants, while for the height and diameter variables the optimal sample size is four plants in the direction of the row considering a semi-amplitude of the confidence interval (D%) equal to 20% of the average. Bulb mass variables require 10 repetitions to assess up to 20 treatments in a randomized block design for the least significant difference of the Tukey’s test, expressed as a percentage of the average of 35%. Bulb height and bulb diameter require just six repetitions for the same assessment.

ABSTRACT. The objective of this study was to estimate the coefficient of repeatability and the number of measurements required for production and quality variables in a strawberry crop. An experiment was conducted with two strawberry cultivars from two origins grown in four substrate mixtures, totaling 16 treatments, evaluated in a randomized block design with four replications. Mass (MF) and number (NF) of fruits per plant were evaluated as measures of production, and total soluble solids (SST), titratable acidity (AT) and firmness (FIR) of fruits during the crop cycle were evaluated as measures of quality. Subsequently, the repeatability coefficient was estimated by the following methods: analysis of variance (ANOVA), principal component analysis using a correlation matrix (PCcor), principal component analysis using a variance-covariance matrix (PCcov) and structural analysis (SA). The number of measurements was adjusted for each studied variable based on determination coefficients of 0.80, 0.85, 0.90, and 0.95. The repeatability coefficients ranged from low to medium. The ANOVA method gave the lowest r values, while the PCcov method presented the highest values of r. When using the PCcov method, 3.6, 2.9, 6.2, 3.2, and 3.8 measurements were needed to reach 80% confidence for the variables MF, NF, SST, AT, and FIR, respectively, and this increased to 7.3, 14.0, 29.6, 15.4, and 18.1 for 95% confidence in the results for MF, NF, SST, AT, and FIR, respectively.

RESUMEN El objetivo de este trabajo fue identificar y estimar las relaciones entre variables componentes de producción y rendi miento de frutos en tomate. El experimento se realizó con diseño de bloques al azar con un arreglo factorial 2x3x3, correspondiendo a dos híbridos de tomate (Netuno y San Vito), tres dosis de boro (H3BO3 - 0, 2, 4 g/sitio) y calcio (si aplicación, aplicación cada 7 días y aplicación cada 14 días), para un total de 18 tratamientos, cuatro repeticiones y 20 plantas por parcela. Se estimaron los coeficientes de correlación de Pearson entre las variables medidas, poste riormente, se seleccionaron aquellos con mayor significancia para la productividad mediante el método Stepwise y la verificación de la multicolinealidad por el número de condiciones y el factor de inflación de la varianza. Las correla ciones de las variables seleccionadas fueron descompuestas en efectos directos e indirectos sobre la productividad de los frutos mediante el análisis de coeficientes de trayectoria. Se encontró una fuerte correlación entre las variables, excluyendo las variables altura, diámetro y masa promedio de los frutos. Por lo tanto, existen relaciones de causa y efecto entre la variable independiente la masa total de frutos y la variable principal de productividad total de frutos, y las variables diámetro y número total de frutos no contribuyeron a aumentar la productividad de tomate.

ABSTRACT The objective of this study was to identify and estimate the relationships between production component variables and fruit yields in tomatoes. This experiment was conducted in a randomized block design with a 2x3x3 factorial arrangement, with two tomato hybrids (Netuno and San Vito), three doses of boron (H3BO3 - 0, 2, 4 g/pit) and three calcium floral applications (no application; application every 7 days; and application every 14 days), totaling 18 treatments with four replications and 20 plants per plot. Pearson correlation coef ficients were estimated between the measured variables and, after that, those with greater significance were selected for productivity with the Stepwise method and verification of multicollinearity using the number of condition and inflation factor of the variance. The correlations of the selected variables were decomposed into direct and indirect effects on fruit productivity with path analysis. There was a strong correlation be tween the variables, excluding the variables height, diameter and average mass of the fruits. Thus, there were cause and effect relationships between the independent variable total mass of the fruits and the principal variable total fruit yield. The variables diameter and total number of fruits did not contribute to an increased tomato production.

Resumo: O objetivo deste trabalho foi avaliar o impacto do tamanho da amostra sobre o diagnóstico da multicolinearidade em análise de trilha. A partir das análises de variáveis produtivas do tomate-cereja, foram obtidas duas matrizes de correlação de Pearson, uma com multicolinearidade severa e outra com multicolinearidade fraca. Sessenta e seis tamanhos de amostra foram delineados e, a partir da amplitude do intervalo de confiança “bootstrap”, verificou-se a existência de interferência do tamanho da amostra na multicolinearidade. Quando o tamanho da amostra foi pequeno, a imprecisão das estimativas dos critérios de diagnóstico interferiu na conclusão quanto à multicolinearidade da matriz com multicolinearidade fraca.

Abstract: The objective of this work was to evaluate the interference of sample size on multicollinearity diagnosis in path analysis. From the analyses of productive traits of cherry tomato, two Pearson correlation matrices were obtained, one with severe multicollinearity and the other with weak multicollinearity. Sixty-six sample sizes were designed, and from the amplitude of the bootstrap confidence interval, it was observed that sample size interfered on multicollinearity diagnosis. When sample size was small, the imprecision of the diagnostic criteria estimates interfered with multicollinearity diagnosis in the matrix with weak multicollinearity.

RESUMO: O objetivo deste trabalho foi determinar o tamanho de amostra necessário para estimar o coeficiente de correlação de Pearson entre variáveis do tomate cereja. Foram instalados dois ensaios de uniformidade em ambiente protegido na primavera/verão de 2014. As variáveis observadas em cada planta foram comprimento médio de fruto, largura média de fruto, peso médio de fruto, número de cachos, número de frutos por cacho, número de frutos e peso total de frutos, sendo calculada a matriz de correlação de Pearson entre elas. Foram planejados 68 tamanhos de amostra em uma estufa e 48 em outra, com tamanho inicial composto de 10 plantas e os demais obtidos acrescentando cinco plantas. Para cada tamanho de amostra planejado foram obtidas 3000 estimativas do coeficiente de correlação de Pearson através de reamostragens “bootstrap” com reposição. O tamanho de amostra de cada coeficiente de correlação foi determinado quando o valor da amplitude do intervalo de confiança de 95% foi menor ou igual a 0,4. A obtenção das estimativas do coeficiente de correlação de Pearson com elevada precisão é difícil para caracteres com relação linear fraca e, consequentemente, maior é o tamanho amostra necessário para estima-los. As relações lineares envolvendo as variáveis relacionadas com o tamanho e o número de frutos por planta tem menor precisão. Para estimar o coeficiente de correlação entre variáveis produtivas do tomate cereja, com intervalo de confiança de 95% igual a 0,4, é necessário amostrar 275 plantas na estufa de 250m², e 200 plantas na estufa de 200m².

ABSTRACT: The aim of this study was to determine the required sample size for estimation of the Pearson coefficient of correlation between cherry tomato variables. Two uniformity tests were set up in a protected environment in the spring/summer of 2014. The observed variables in each plant were mean fruit length, mean fruit width, mean fruit weight, number of bunches, number of fruits per bunch, number of fruits, and total weight of fruits, with calculation of the Pearson correlation matrix between them. Sixty eight sample sizes were planned for one greenhouse and 48 for another, with the initial sample size of 10 plants, and the others were obtained by adding five plants. For each planned sample size, 3000 estimates of the Pearson correlation coefficient were obtained through bootstrap re-samplings with replacement. The sample size for each correlation coefficient was determined when the 95% confidence interval amplitude value was less than or equal to 0.4. Obtaining estimates of the Pearson correlation coefficient with high precision is difficult for parameters with a weak linear relation. Accordingly, a larger sample size is necessary to estimate them. Linear relations involving variables dealing with size and number of fruits per plant have less precision. To estimate the coefficient of correlation between productivity variables of cherry tomato, with a confidence interval of 95% equal to 0.4, it is necessary to sample 275 plants in a 250m² greenhouse, and 200 plants in a 200m² greenhouse.